1. Field of the Invention
The present invention relates to a technique for determining the local conductivity of an object or patient by combining the techniques used for magnetic resonance current density imaging (MRCDI) with the techniques used for electrical impedance tomography (EIT).
2. Description of the Prior Art
The techniques of electrical impedance tomography (EIT) and magnetic resonance current density imaging (MRCDI) are generally known by those skilled in the art.
EIT (also called xe2x80x98applied potential tomographyxe2x80x99) is a technique that determines the internal conductivity or impedance of a patient or an object by applying and measuring a surface current while simultaneously measuring the surface potential. EIT has applications in medicine and process control. The major limitations of EIT are its low spatial resolution, and, in the medical field, the large variability of images between subjects. Recordings are typically made by applying current to the body or object under test using a set of electrodes and measuring the voltage developed between other electrodes. To obtain reasonable images, at least one hundred, and preferably several thousand, such measurements must be made.
For medical applications, EIT produces images of the distribution of impedivity (or, more commonly, resistivity), or its variation with time or frequency, within the tissue of the patient. There is a large resistivity contrast (up to about 200:1) between a wide range of tissue types in the body, making it possible to use resistivity to form anatomical images. Furthermore, there is often a significant contrast between normal and pathological tissue. For example, it is known that, at 1 kHz, cerebral gliomas have a resistivity about half that of normal tissue. To measure resistivity or impedivity, an excitation current must flow in the tissue and the resulting voltages measured. In practice, almost all EIT systems use constant current sources, and measure voltage differences between adjacent pairs of electrodes. To obtain an image with good spatial resolution, a number of such measurements is required. This can be achieved by applying different current distributions to the body, and repeating the voltage measurements. From the set of measurements, an image reconstruction technique generates the tomographic image. Mathematically, the known quantities are the voltages and currents at certain points on the body; the unknown is the impedivity or resistivity within the body. At low frequencies, these quantities are related by Poisson""s equation:
∇xc2x7"sgr"∇xcfx86=0
where "sgr" is the conductivity (admittivity may be represented by a complex "sgr"), xcfx86 is the potential and ∇ is the Poisson operator, "sgr" and xcfx86 are spatial fields whose magnitudes are functions of position, and xcfx86 is also a non-linear function of "sgr". In practice, the solution of Poisson""s equation is very sensitive to noise in the measurements, and normalization techniques must be used. Most in-vivo images have been produced using linearized, approximating techniques. These techniques attempt to find a solution for a small change in resistivity from a known starting value. Until recently, the change in resistivity was measured over time, and EIT images were inherently of physiological function. It is now possible to produce anatomical images using the same reconstruction technique, by imaging changes with frequency.
On the other hand, in MRCDI, static or radio-frequency currents are applied to the patient or object of interest so as to produce a magnetic field which can be imaged using conventional MRI techniques. A standard spin echo pulse sequence is used, with an addition of a bipolar current pulse. The flux density parallel to the main magnetic field, generated by the current pulse, is encoded in the phase of the complex MR image. The spatial distribution of magnetic flux density is then extracted from the phase image. Current density distribution generated by repetitive current flow synchronized to the imaging sequence is imaged, and current density is calculated by knowing the magnetic flux density.
Using MRCDI, current densities as low as 1 microamp/mm2 can be imaged satisfactorily, even near the current carrying electrodes. To reconstruct the current density in one direction, components of magnetic flux density in at least two orthogonal directions are needed. Using MRCDI, only the B field component parallel to the main magnetic field can be imaged. Therefore, the sample must be rotated to align two of its axis with the direction of the main magnetic field, one axis at a time. This is the major limitation of the technique in applying it to human subjects or large samples. To overcome this limitation, Scott et al. in a paper entitled Rotating Frame RF Current-Density Imaging, Magnetic Resonance in Medicine, Vol. 33, pp. 355-369 (1995) implemented a technique in which current density at Larmor frequency and parallel to the main magnetic field can be imaged without rotating the sample to be imaged. However, imaging current densities at RF frequencies (e.g. approximately 86 MHZ at 2 Tesla) may not provide biologically useful information as much as dc current density imaging does. It is also possible to use open-magnet MR imaging systems to eliminate the problem of object rotation.
It is desired to simultaneously provide high-resolution images of impedance and of electrical current density images. It is also desired to image very low currents, on the order of 1 microamp/mm2. The present invention has been designed to meet these needs in the art.
The above and other objects of the invention have been met by development of a technique, referred to herein as magnetic resonance-electrical impedance tomography (MREIT), for determining the local conductivity of an object. The MREIT technique of the invention combines magnetic resonance current density imaging (MRCDI) with electrical impedance tomography (EIT) in order to obtain the benefits of both procedures. In particular, the method of the invention includes the step of current density imaging by performing the steps of placing a series of electrodes around the patient or object to be imaged for the application of current, placing the patient or object in a strong magnetic field, and applying an MR imaging sequence which is synchronized with the application of current through the electrodes. The electric potentials of the surface of the object or patient are measured simultaneously with (or following) the MR imaging sequence, as in EIT. Then, the MR imaging signal containing information about the current and the measured potential are processed to calculate the internal conductivity (impedance) of the object or patient.
Determination of the local conductivity of the patient or object begins with a mapping of the current density for a particular pair of electrodes. The equi-potential lines are then determined using the measured surface potential data. These equi-potential lines represent an area with a constant potential and are substantially perpendicular to the current density lines. The gradient of the potential is then readily calculated from the equi-potentials.
The intersection of the constant current lines and the equi-potential lines form a grid, where the local impedance may be determined from the grid points by the relationship:             j      →        ⁡          (              x        ,        y        ,        z            )        =                    σ        ⁡                  (                      x            ,            y            ,            z                    )                    ·                        ∇          →                ⁢        φ              ⁢          xe2x80x83        ⁢          (              x        ,        y        ,        z            )      
where       j    →    ⁡      (          x      ,      y      ,      z        )  
is the local current density, "sgr"(x,y,z) is the local impedance, and             ∇      →        ⁢    φ    ⁢      xe2x80x83    ⁢      (          x      .      y      .      z        )  
is the gradient of the potential.
In another approach, first an EIT image of the conductivity distribution is obtained. An iterative approach is adopted by taking the EIT image as an initial conductivity distribution "sgr"i(x,y,z). For this conductivity distribution, the EIT forward problem is solved and the potential distribution xcfx86(x,y,z) and gradient of the potential field             ∇      →        ⁢    φ    ⁢      xe2x80x83    ⁢      (          x      ,      y      ,      z        )  
are found. For a given conductivity distribution, (which can be assumed to be equal to "sgr"i(x,y,z)), the gradient of the potential field,                     ∇        →            ⁢      φ        ⁢          xe2x80x83        ⁢          (              x        ,        y        ,        z            )        ,
can also be determined from MRCDI measurements. Minimizing the error between the two values of                     ∇        →            ⁢      φ        ⁢          xe2x80x83        ⁢          (              x        ,        y        ,        z            )        ,
an optimum expression for "sgr"(x,y,z), is obtained. The algorithm is iterated for the new distribution of "sgr"(x,y,z), until a minimum error is obtained.